Spatial Mechanical Systems Research Articles

Spatial Transient Analysis of Inertia-Variant Flexible Mechanical Systems

An analytical method for transient dynamic simulation of large-scale inertia-variant spatial mechanical and structural systems is presented. Multibody systems consisting of interconnected rigid and flexible substructures which may undergo large angular rotations are analyzed. A finite element technique is used to characterize the elastic properties of deformable substructures. A component mode technique is then employed to eliminate insignificant substructure modes. Nonlinear holonomic constraint equations are used to define joints between different substructures. The system equations of motion are written in terms of a mixed set of modal and physical coordinates. A generalized coordinate partitioning technique is then employed to eliminate redundant differential equations. An implicit-explicit numerical integration algorithm solves the remaining set of differential equations and the approximate physical system state is recovered. The transient analysis of a spatial vehicle with flexible chassis is presented to demonstrate the method.

The derivation of general kinematic equations of spatial constrained mechanical systems with the aid of a computer

The kinematic solution of constrained spatial mechanical systems esp., of spatial mechanisms with nonconstant velocity ratio is usually carried out numerically with the aid of a computer. As far as the analytical solution is concerned, we are still forced to use hand computation although there exist general methods and procedures which enable us to obtain the starting kinematic equations of motion. This step is a frequent source of errors, because essentially we must multiply a great number of matrices of the type (4 × 4) whose elements are, in general, trigonometric expressions. The aim of this paper is to introduce a method that enables us to obtain the mathematical model automatically with the aid of a computer using only basic information about dimensions and variables. The procedure is based on the application of the transformation matrices of basic motions [1,2] and of the programs for symbolic operations with matrices [3].